Write and solve a quadratic equation. A right triangle has a hypotenuse of 105 inches. One leg is forty-two inches less than double the other leg. What is the length of the shorter leg? (Hint: a^2+b^2=c^2)
I just need help with this question. If you could show step by step that would be perfect thanks!
The "other" leg is the shorter leg, which we'll call, S
Then the longer leg = 2S - 42
Using pythag theorem, , we get:
------ FOILing
------ Replacing - 168S with - 315S + 147S
5S(S - 63) + 147(S - 63) = 0
(S - 63)(5S + 147) = 0
S - 63 = 0 OR 5S + 147 = 0
S, or length of the shorter leg = OR (ignore)
** You could also solve this quadratic equation by: using the quadratic equation formula, COMPLETING THE SQUARE, or GRAPHING. However, graphing is most-often not used.